What is the integral of (5cos(x)+3sin(x)) ?

The integral of (5cos(x)+3sin(x)) is 5sin(x)-3cos(x)+C

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integral of (5cos(x)+3sin(x))

\int (5 cos (x) + 3 sin (x)) d x

5 sin (x) - 3 cos (x) + C

Solution steps

\int 5 cos (x) + 3 sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 cos (x) d x + \int 3 sin (x) d x

\int 5 cos (x) d x = 5 sin (x)

\int 3 sin (x) d x = - 3 cos (x)

= 5 sin (x) - 3 cos (x)

Add a constant to the solution

= 5 sin (x) - 3 cos (x) + C

\int e^{- 5 x} + 2^{x} d x

\int \frac{3 x}{x ^{2} + 3} d x

\int \frac{( x ^{- \frac{1}{3}} )}{1 + x ^{\frac{2}{3}}} d x

\int \frac{1}{9 + 4 x} d x

\int \frac{3 x ( 3 x + 2 ) + 4}{x ^{4} + 2 x ^{2}} d x

What is the integral of (5cos(x)+3sin(x)) ?
The integral of (5cos(x)+3sin(x)) is 5sin(x)-3cos(x)+C